Question:

(a) (I) The following equations relate to the market conditions for pullovers at a given point of time:

Demand Function: Q_d = 1200 - P
Supply Function: Q_s = 600 + 4P

Calculate:

(i) the total revenue obtainable when the market clears
(ii) consumer surplus at the market-clearing price
(iii) the ratio of tax payable between consumers and producers if the government introduces a tax of Rs 20 on pullovers.

(II) With more information, the following extended demand function for pullovers was generated (where Y is income and Pg is the price of a related product:

Q_d = 1800 - 1.5P + 0.02Y - 0.4Pg
If the initial conditions provided are such that P = Rs 400, Y = Rs 20,000 and Pg = Rs 200, calculate the price, income and cross elasticities of demand and comment on the nature of the product and its relationship with the related good.

(b) Using the theory of demand, explain how you would model the demand for health care services in your locality. You are also required to explain the expected signs on variables that you have included in your modeling.